Some new Z-cyclic whist tournaments

Abstract

While the existence of whist tournaments for v players, Wh(v), is known for all v ≡ 0, 1 (mod 4), knowledge regarding Z-cyclic Wh(v) is incomplete. By results of Finizio and of Anderson, Finizio and Odoni, each new prime q ≡ 3 (mod 4) for which a Z-cyclic Wh(q²) is found provides an infinite class of new values for which Z-cyclic whist tournaments are known to exist. We construct Z-cyclic Wh(q²) for q = 7, 11, 19, 23 and 31 by a method that promises to be effective also for all larger primes q = 3 (mod 4).